Page 541 - Modelling in Transport Phenomena A Conceptual Approach

A.8. METHODS OF INTEGRATION 521

“able A.4 Roots and weight factors for Gauss-Laguerre quadrature (Abramowitz
and Stegun, 1970).

n Roots (~i) Weight Factors (wi)
0.58578 64376 27 0.85355 33905 93
3.41421 35623 73 0.14644 66094 07
0.41577 45567 83 0.71109 30099 29
2 2.29428 03602 79 0.27851 77335 69
6.28994 50829 37 0.01038 92565 02
0.32254 76896 19 0.60315 41043 42
1.74576 11011 58 0.35741 86924 38
4.53662 02969 21 0.03888 79085 15
9.39507 09123 01 0.00053 92947 06
0.26356 03197 18 0.52175 56105 83
1.41340 30591 07 0.39866 68110 83
4 3.59642 57710 41 0.07594 24496 82
7.08581 00058 59 0.00361 17586 80
12.64080 08442 76 0.00002 33699 72

Solution
Since a = 0, then
p=U
and
F(u) = J;I

The four-point quadrature w given by

The values of wi and F(ui) are given an the table below:

i ai wi F(Ui) = 6 WiF(Uj)
0 0.32254769 0,603 15410 0.56793282 0 a25510 1
1 1.74576110 0.35741869 1.32127253 0.47224750
2 4.53662030 0.03888791 2.12993434 0.08282869
3 9.39507091 0.00053929 3.06513799 0.00165300

=
r(i.5) = f3 wi~(ui) 0.8992802
i=O
The exact value of r(1.5) b 0.8862269255.